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Trivial andNon Trivial

Dependencie

s Reporter:Pangan, Carolina F.

III - 10

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Trivial Dependency

A dependency is triviali! it cannot possi"ly not"e satis#ed.

$ %&, P& ' -( %&

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)on Trivial

DependencyT*ey are t*e ones t*atcorresponds togen+ine integrityconstraints.

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Closure of A

Set ofDependencies

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%oe FDs ig*t iply

ot*ers:$ %&, P& ' -( $ CIT, T '

Iplies "ot* o! t*e !ollo/ing:

$ %&, P& ' -( CIT

$ %&, P& ' -( T

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Transitive F+nctionalDependency

Relvar R /it* t*ree attri"+tes A, andC.

A -( and -( C "ot* *old !or R

T*en it is easy to see t*at

A -( C also *olds !or R

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Arstrongs A2ios

1.Re3e2ivity

I! is a s+"set o! A, t*en A -(

.4.A+gentation

I! A -( , t*en AC -( C.

5.TransitivityI! A -( and -( C, t*en A -( C.

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6.%el!-deterination

A -( A

7.DecopositionI! A -( C, t*en A -( and A -( C

8.9nionI! A -( and A -( C, t*en A -( C

.CopositionI! A -( and C -( D, t*en AC -(

D.

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;eneral 9ni#cationT*eore

I! A -( and C -( D, t*en A 9 $ C < ' -( D

$=*ere 9 is +nion and - is seto! di>erence'

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Pro"le:

%+ppose /e are given relvar R /it*attri"+tes A, , C, D, ?, F and t*e

FDs:

A -( C

-( ?CD -( ?F

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A < eployee n+"er < departent n+"er

C < anagers eployee n+"er

D < pro@ect n+"er? < departent nae

F < percentage o! tie

AD -( F *olds !or R

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Ans/ers

1. A -( C $;IB?)'

4. A -( C $ D?CP%ITI) '

5. AD -( CD $ A9;?)TATI) '6. CD -( ?F $;IB?)'

7. AD -( ?F $ TRA)%ITIBIT '

8. AD -( F $ D?CP%ITI) '